J. Phys. Chem. 1995,99, 12341-12348
12341
Solid-state 1 7 0 Magic-Angle and Dynamic-Angle Spinning NMR Study of the Si02
Polymorph Coesite
P. J. Grandinetti*
Department of Chemistry, The Ohio State University, 120 W. 18th Avenue, Columbus, Ohio 43210-1173
J. H. Baltisberger
Department of Chemistry, CPO 86, Berea College, Berea, Kentucky 40404
I. Farnant and J. F. Stebbins
Department of Geological and Environmental Sciences, Stanford University, Stanford, Califomia 94305
U. Werner$ and A. Pines
Materials Sciences Division, Lawrence Berkeley Laboratory and Department of Chemistry,
University of Califomia, Berkeley, Califomia 94720
Received: January 6, 1995; In Final Form: March 21, 1 9 9 9
Five distinctly resolved I7O solid-state NMR resonances in room temperature coesite, an Si02 polymorph,
have been observed and assigned using dynamic-angle spinning (DAS) at 11.7 T along with magic-angle
spinning (MAS) spectra at 9.4 and 11.7 T. The I7O quadrupolar parameters for each of the five oxygen
environments in coesite are correlated with the Si-0-Si bridging bond angles determined by diffraction
experiments. The sign of e2qQ/h along with the orientation of the electric field gradient for oxygen in the
Si-0-Si linkage were determined from a Townes-Dailey analysis of the data.
1. Introduction
The recent application of I7O dynamic-angle
(DAS) nuclear magnetic resonance (NMR) spectroscopy to both
crystalline and amorphous silicates has provided a considerable
amount of new information conceming the short- and mediumrange structures around oxygen in these material^.^-^ One type
of information is in the form of I7O quadrupolar coupling
parameters, which are a measure of the electric field gradient
(efg) tensor at the oxygen nucleus. Knowledge of the efg tensor
can be related to the local distribution of electrons and the
arrangement of charge on neighboring atoms or ions, thus
providing insight into the character of the chemical bonds and
the bonding wave functions. In general, the calculation of the
efg tensor at a particular nucleus in a solid requires knowledge
of the ground-state electronic wavefunction and all atomic
positions. While a full ab initio calculation can be problematic
in solids, it has been shown that small clusters modeling silicate
tetrahedral linkage can be effective models for bonding in solid
silicate^.^,^ Indeed, I7O efg tensors calculated using hb initio
methods in a number of small clusters exhibit trends that
correlate well with experimentallymeasured efg tensors in solid
silicate^.'^-'^ Another approach that is less exact but has the
advantage of providing analytical expressions for correlating
efg tensors to structure is the Townes-Dailey modeli4 for
calculating efg tensors. This approach was first applied to I7O
efg tensor data measured by NMR in borates and silicates by
~
~~~
* To whom correspondence should be addressed.
Present address: Centre de Recherches sur la Physique des Hautes
Temperatures, 1D Ave de la Recherche Scientifique, 45071 Orleans CEDEX
2, France.
Present address: Department of Chemistxy, Indiana University, Bloomington, IN 47405.
Abstract published in Advance ACS Abstracts, July 1, 1995.
@
Bray and c o - ~ o r k e r and
s ~ ~in~a ~number
~
of zeolites and related
materials by Oldfield and c o - w o r k e r ~ . ' ~Unfortunately,
*'~
the
lack of a large database of I7O quadrupolar coupling parameters
made it difficult to further refine the application of ab initio or
the Townes-Dailey approaches to I7O efg tensor calculations
in silicates. The recent advent of DAS, however, has considerably improved this situation.
In this paper we present solid-state I7O NMR results on the
silica polymorph coesite. Coesite is an ideal solid for confirming the correlations between the measured I7O quadrupolar
coupling parameters and the oxygen environment. From
diffraction s t ~ d i e s ~coesite
~ - ~ ~is known to have five distinct
oxygen sites in a ratio of 1:1:2:2:2, with Si-0-Si bridging
bond angles of 180.00", 142.56", 144.46", 149.53", and 137.22",
respectively. This set of bridging bond angles provides a good
range over which to check the correlations between Si-0-Si
angle and I7O quadrupolar parameters.
2. Experimental Procedures
2.1. Coesite Preparation and Characterization. I7Olabeled coesite (Si02) was made by first reacting S i c 4 with
40% 170-labeledH20. The products of Si02, HC1, and residual
H20 were then heated to 1000 "C to remove the HC1, H20,
and any other impurities, leaving pure silica. This sample was
welded into a pt capsule with a small amount (1-3%) of H20
(unenriched) to speed kinetics and then heated in a piston
cylinder apparatus at 900 "C and 35 kbar to transform the SiOz.
Slow recrystallization at these elevated pressures over 24 h
allowed for the formation of a nearly pure coesite phase sample.
Attempts to add Fez03 impurities to act as an NMR relaxing
agent were unsuccessful, and therefore, an undoped sample was
prepared for the final experiments. The samples was character-
0022-365419512099-12341$09.0010 0 1995 American Chemical Society
12342 J. Phys. Chem., Vol. 99, No. 32, I995
Grandinetti et al.
Residuals
~ . ~ . ~ I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -. ~ -~ ~- I .I ~ -~ . P, ~ ~~ , ~. ~ ~~ ~ , , ~- ~ .~ ~~ , ~~ ,
-50.0
00
50.0
-100.0
50.0
0.0
-50.0
ppm (from H2I70)
100.0
-1500
ppm (from H2'70)
-100.0
Figure 1. Magic-angle spinning (MAS) spectra and simulations of 170in coesite at (a) 9.4 T (54.544 MHz) and (b) 11.7 T (67.797 MHz). All
spectra are referenced relative to I70-labeled H20. The simulation at 9.4 and 11.7 T were generated using the parameters in Table 1.
01:x x
163: x x
163: Y Y
rf
165: x
rotor
axis
54.74'
37.38'
'
1
P O
-1
\
I
Y
X X Y Y
X X Y Y x x
xxxxxxx
(Cosine)
(Sine)
Y Y Y Y Y Y Y Y
79.19'
angle
Y
Y Y
\
I
xxxxxxxx
YPPYYYPY
gR:X x x x x x x x
Y Y Y P Y P Y Y
\
xxxxxxxx
Y Y Y Y Y Y Y Y
~
Figure 2. Pulse sequence, coherence transfer pathway, and minimal phase cycle for MAS-detected shifted-echo dynamic-angle spinning. 91, 43,
and 45 are the rf phases of the pulses shown above, and & is the receiver phase.
ized by both powder X-ray diffraction and 29SiMAS NMR at
9.4 T. The powder X-ray diffraction pattem showed only a
coesite phase with no significant impurities. The 29Si MAS
spectrum (not shown) agreed with previously published spectraz2
with peaks at - 108.3 and - 114.1 k 0.1 ppm relative to extemal
tetramethylsilane.
2.2. NMR Spectroscopy. All experiments at 11.7 T were
performed on a Chemagnetics CMXSOO spectrometer using a
modified version of a home-built DAS probe described earlierSz3
All experiments at 9.4 T were performed on a Varian VXR400S
spectrometer with a commercial (Doty Scientific, Inc.) 5 mm
high-speed MAS probe. All experiments were done at ambient
temperature with sample spinning rates between 13 and 15 kHz.
The integrated intensities of the spinning sidebands were less
than 12% of the total intensity at 11.7 T. The I7OTI relaxation
time of approximately 100 s for all sites was measured at 11.7
T for coesite using a saturation recovery experiment.
Bloch decay experiments were used to obtain the 29SiMAS
spectra. The Hahn echo sequence (90-t- 180-acquire) was
used to collect the I7O MAS spectra at both 9.4 and 11.7 T.
The recycle delays were set to 3600 and 1000 s, reepectively.
The I7O MAS spectra are shown in Figure 1.
The DAS angle pair (37.38', 79.19') was employed in
removing the second-order anisotropic broadenings, while
detection was carried out at 54.74' to eliminate all chemical
shift anisotropy contributions to the anisotropic line shapes.24
The DAS pulse sequence employed is a modification of the
hypercomplex shifted echo DAS sequence25and is shown in
Figure 2. A DAS rotor reorientation time of 60 ms was used.
To ensure selectivity of the I7O central transition, d 2 times of
8.5 ps (at 37.38'), 7.5 ps (at 54.74'), and 6.5 ,us (at 79.19')
were employed. The DAS echo was shifted by Tech0 = 1.5 ms.25
With a relaxation delay of 900 s between scans, 32 scans were
averaged for each of the 47 x 256 hypercomplex tl x t:! points
acquired. The dwell time in t 2 was 90.9 ps (1 1.1 kHz) and in
tl was 100 ps (10 kHz). The tl dimension was zero-filled to
256 points, and no apodization was applied to tl dimension to
try to retain the highest resolution possible; truncation artifacts
("sinc" wiggles) may be seen in the 2D DAS spectrum. The
I7O DAS spectrum is shown in Figure 3.
3. Results
3.1. NMR Data Reduction. For spin > 1/2 nuclei like I7O,
the quadrupolar coupling between its nuclear quadrupole
moment and surrounding electric field gradient leads to an
orientation dependence of its NMR transition frequency, which
in a polycrystalline sample results in a characteristic line shape
that can be analyzed to obtain the nuclear quadrupolar coupling
parameters. In a static sample NMR experiment on a multisite
system like coesite, these characteristic anisotropic NMR line
shapes are overlapping, and therefore, the spectrum is not easily
analyzed. Although MAS is designed to eliminate and effectively separate the anisotropic line shapes due to first-order
perturbations like dipolar coupling and chemical shift, for I7O
the magnitude of quadrupolar coupling is often large enough
that anisotropies due to second-order perturbations, which cannot
be eliminated with MAS, are present. Therefore, I7O MAS
cannot completely eliminate and separate the anisotropic line
shapes in coesite. However, with DAS both the first- and
second-order orientation dependences are removed from the
central 112 -1/2 NMR transition of I7O and the anisotropic
NMR line shapes separated in a two-dimensional DAS spectrum.
The coesite MAS and DAS spectra were fit using a powder
line shape simulation based on an algorithm described previouslyZ6and the CERN library MINUIT least-squares minimization subroutines. xiduced
was determined using the noise in the
baseline to estimate the error at each point in the spectrum. For
all parameters we report larger uncertainties than those obtained
from the first and second derivatives of x
: at the~ minimum
~ ~
to account for the minor line shapes distortions due to finite
spinning speeds, slight angle missettings, saturation effects, and
other intensity distortions that are difficult to quantify.
The I7O NMR parameters for the five oxygen sites in coesite
obtained by fitting the DAS separated second-order quadrupolar
-
~
~
I7O NMR of Si02 Polymorph Coesite
.
I
Phys.
.
Chem., Vol. 99, No. 32, 1995 12343
I
a0
60
40
20
J
I ' " I . ' ~ I ' " I " ' I " .
0
-20 -40 -60 -80
Frequency @pm)
60 40 20
0 -20-40-60-80
Frequency@pm)
Figure 3. Two-dimensional DAS spectrum of I7O in coesite at 11.7 T. The projection of the isotropic shift dimension is shown at the top. The
contour lines are drawn at levels of 7, 16, 25, 34, 43, 52, 61, 71, 79, 88, and 97% of the maximum point in the spectrum. The spectrum is
referenced relative to 170-labeledH20. Also shown are cross sections from the two-dimensional DAS spectrum taken parallel to the anisotropic
(54.74') dimension for the five sites in coesite. "Best-fit'' simulations of the five sites are shown alongside each cross section. Best-fit quadrupolar
and chemical shift parameters are listed in Table 1.
TABLE 1: Quadrupolar Coupling Parameters and Isotropic Chemical Shifts for the Five Oxygen Sites in Coesite Obtained
from Least-Squares Fits of the 11.7 and 9.4 T MAS and 11.7 T DAS Spectrau
e
~
(PPm)
-19.24 f 2.00
1.54 f 2.00
12.87 f 2.00
17.92 f 2.00
21.93 f 2.00
c, (MHz)
rl
42 (PPm)
6.05 f 0.05
5.43 f 0.05
5.52 f 0.05
5.45 f 0.05
5.16 f 0.05
0.000 It 0.005
0.166 f 0.005
0.169 f 0.005
0.168 f 0.005
0.292 f 0.005
29 f 1
41 f 1
53 f 1
57% 1
58f 1
intensity
0.83 f 0.1
1.05 f 0.1
2.05 f 0.1
2.16 f 0.1
1.90 f 0.1
assignment
01
02
04
03
05
a Because of the difficulties associated with extemal shift references, we report an uncertainty of f2.00 in ,
:iS
accurate to within fO.l ppm. Minimum x
: obtained
~ ~was <5.
~ ~ ~ ~
line shapes to single site line shapes and by ,fitting the 11.7 and
9.4 T MAS spectra to five overlapping second-order quadrupolar
line shapes were in agreement within our experimental error
and are listed in Table 1. The simulated anisotropic line shapes
obtained with the parameters in Table 1 are shown along with
the experimental MAS spectra in Figure 1 and along with the
experimental DAS cross sections in Figure 3. While the signalto-noise and least-squares fit are better for the MAS spectra
than for the anisotropic DAS cross sections, without the DAS
results it is difficult to justify that our MAS least-squares fit is
the only unique fit for the MAS line shape.
It should be pointed out that to a small extent the quadrupolar
asymmetry parameter 7 can be "exchanged" for Gaussian or
Lorentzian line broadening without affecting the overall
x : significantly.
~ ~ Therefore,
~ ~ the
~ line~ broadening for each
site was not allowed to vary in the least-squares fit and was
held fixed at 30 Hz Lorentzian and 145 Hz Gaussian.
3.2. Assignments. Assignments of the five I7O resonances
to the five crystallographically distinct oxygens is based on the
integrated intensities of the resonances and the empirical
correlation7 that the I7O quadrupolar coupling constant, C, =
e2qQ/h, increases with increasing Si-0-Si angle, while the
170quadrupolar coupling asymmetry parameter, 7,decreases
with increasing Si-0-Si angle. These correlations derive from
both theoretical ab initio calculations on small clusters modeling
silicate tetrahedral linkage''.'o as well as experimental I7ONMR
results on other crystalline silicate system^.*^,^^
Detailed illustrations of the structure of coesite can be found
in previous diffraction s t ~ d i e s . ' ~ -From
~ ' these studies coesite
LSi-0-Si
180.00"
142.56'
149.53'
144.46'
137.22'
however, relative shifts are
is known to have five distinct oxygen sites in a ratio of 1:1:2:
2:2 with Si-0-Si bridging bond angles of 180.00', 142.56',
144.46', 149.53', and 137.22', respectively. This is in good
agreement with the ratio of the integrated intensities for the five
resonances in coesite. Therefore, the two low-intensity signals
near 0 and -20 ppm must correspond to crystallographic sites
0 1 (180.00") and 0 2 (142.56"). Of these two resonances the
one near -20 ppm has the largest quadrupolar coupling constant
and smallest asymmetry parameter and is therefore assigned to
the 0 1 site. This means that the peak near 0 ppm must
correspond to 0 2 .
The other three crystallographic sites may be partially
assigned by assuming that the site with the smallest bridging
bond angle, 0 5 (137.22'), is assigned to the resonance near
22.3 ppm, which has the largest asymmetry parameter and
smallest quadrupolar coupling constant. The remaining two
sites, 0 4 (149.53") and 0 3 (144.46'), must correspond to the
two peaks near 13 and 18 ppm, respectively, based on their
quadrupolar coupling parameters. The distinction between 0 4
and 0 3 is weaker since both the bond angles and the quadrupolar
coupling parameters are very similar.
4. Analysis
We follow the Townes-Dailey modelI4 as outlined by Bray
and ~ o - w o r k e r s ~and
~ - ~Oldfield
~ , ~ ~ and c o - ~ o r k e r s ~for~ ~ ' ~
calculating the relationship between the efg of I7O and angle
in a Si-0-Si
linkage. In this model the bonding and
nonbonding valence electrons of oxygen in a Si-0-Si linkage
Grandinetti et al.
12344 J. Phys. Chem., Vol. 99, No. 32, 1995
surrounding atoms in the crystal lattice; however, as pointed
out by Jellison et al.,I5 the lattice contribution can be ignored
for the bridging oxygens, where the local contribution is an order
of magnitude stronger.
Using the matrix elements in Table 2, we obtain
Y
Y
where e421 is the I7O quadrupolar coupling constant (Cq21 =
e2q21Q/h = 20.88 MHz) measured3I in atomic oxygen due to
one unbalanced p electron, including Stemheimer effects.32
For a symmetric linkage, such as Si-0-Si, we assume that
n3 = n 4 = 1134, and then R2*1 = 0 and the field gradient R2m is
diagonal. However, we cannot assume that the Z axis of the
efg principal axis system (PAS)is the same as the MO z axis.
Two other possibilities exist for the assignment of the efg PAS
Z axis. One is obtained by a rotation of the tensor Rzm such
that x y, y z, and z x. This transformation is represented
as
- -
-
-
The other possibility is a rotation that takes x
z y. With this rotation we obtain
- z,
y
+
x , and
Therefore, we consider three cases (recalling that in the efg
PAS C, = eQ(Rno)/h and qCq = &eQ(Rz*z)/h).
which form molecular orbitals (MO) with the atomic orbitals
of silicon. Here y = cot 8/2, where 8 is the Si-0-Si bond
angle. The fractional s character, fs, of the sp" (1 5 n 5 2)
hybrid orbitals can be related to y or 8 according to
Iq2), 1$~),and 1yh) are the sp" hybrid orbitals. 1q3) and l v 4 )
form o-bond MO's with silicon, while I ~ I )and 1v2) may form
n-bond MO's with the d orbitals of silicon.30 A schematic
representation of these orbitals is shown in Figure 4.
The efg that arises from nk electrons (0 Ink I2) in the kth
orbital is given by
I
( ~ k 1 ~ qk)
2 m = nk&i*aj(4i1~2m14j)
ij
(11) MO y-axis is efg PAS Z axis:
(3)
where ai are the orbital coefficients and the matrix elements
(dilE2mldj) are given in Table 2. The total efg that arises from
all the bonding and nonbonding valence electrons is
( ~ 2 m=
) ~ ( V ~ I E Z ~ I V ~ )
(I) MO z axis is efg PAS Z axis:
(4)
k
Other contributions to the efg can arise from the charges on
(111) MO x-axis is efg PAS Z axis
qc,,,= - h 3 4
- n , ) + (n34 - n,lf,(@
(16)
47"qC,,, = 3 ( n 3 4 - nllf,(e)
(17)
We have two experimentally measured parameters, ICq[and
171, and in each of the above cases we have three unknown
” 0 NMR of Si02 Polymorph Coesite
J. Phys. Chem., Vol. 99, No. 32, 1995 12345
TABLE 3: Orbital Populations Differences Obtained from a Tomes-Dailey Analysis of the 1 7 0 Quadrupolar Coupling
Parameters for the Five Oxygen Sites in Coesite!
Case I: MO z is PAS z
Case 11: MO y is PAS z
Case 111: MO x is PAS z
- nl
6.05
-6.05
0.000
0.000
0.290
-0.290
- n2
01,
0.290
-0.290
0.169
0.169
-0.169
-0.169
0.279
-0.279
0.249
-0.249
04,
0.269
-0.269
0.302
-0.302
es,-o-s,= 149.530
5.52
-5.52
5.52
-5.52
0.168
0.168
-0.168
-0.168
0.276
-0.276
0.246
-0.246
03,
0.275
-0.275
0.307
-0.307
es,-o-s,= 144.460
5.45
-5.45
5.45
-5.45
0.166
0.166
-0.166
-0.166
0.274
-0.274
0.246
-0.246
02,
0.278
-0.278
0.310
-0.310
es,-o-sI= 142.560
5.43
-5.43
5.43
-5.43
0.292
0.292
-0.292
-0.292
0.271
-0.27 1
0.223
-0.223
05,
0.264
-0.264
0.320
-0.320
esI-o-s,= 137.220
5.16
-5.16
5.16
-5.16
rl
Cq (MHz)
n34
n34
n34
- nl
n34
- n2
n34
- nl
n34
- n2
es,-o-s,= 1800
0.000
0.000
0.030
-0.030
-0.030
0.030
0.029
-0.029
-0.029
0.029
0.029
-0.029
-0.029
0.029
0.048
-0.048
-0.048
0.048
-0.290
0.290
O.Oo0
O.OO0
0.290
-0.290
-0.269
0.269
-0.302
0.302
-0.032
0.032
0.032
-0.032
0.251
-0.25 1
0.320
-0.320
-0.275
0.275
-0.307
0.307
-0.033
0.033
0.033
-0.033
0.255
-0.255
0.327
-0.327
-0.278
0.278
-0.310
0.310
-0.033
0.033
0.033
-0.033
0.257
-0.257
0.331
-0.331
-0.057
0.057
0.057
-0.057
0.225
-0.225
0.359
-0.359
-0.264
0.264
-0.320
0.320
,
Three different cases are considered for the orientation of the efg along with both signs of the quadrupolar coupling constant and asymmetry
parameter. Changing the sign of the asymmetry parameter is equivalent to exchanging the x and y axes of the efg PAS.
parameters (nl, n2, 1134). By making an assumption about the
charge on the oxygen, we can solve for all three parameters;
however, as an intermediate step we will solve for the
differences 1134 - nl and 1134 - n2 which can be obtained from
just IC,l and 171 alone.
TABLE 4: Average Orbital Populations Differences
Obtained from a Townes-Dailey Analysis of the I7O
Quadrupolar Coupling Parameters for the Five Oxygen Sites
in Coesite
Case I:
Case 11:
Case 111:
MO z is PAS z
M O y is PAS z
M O x is PAS z
(I) MO z axis is efg PAS Z axis:
C,
n34
- nl = qJCq2lr+3
3
(11) MO y axis is efg PAS Z axis:
(111) MO x axis is efg PAS Z axis:
n34
- n , = - C J C , 2 ’ 6 L ( 211
e)
In Table 3 are the population differences obtained for the five
oxygen sites in coesite. For each of the 3 cases there are 2
possibilities for the sign of Cq and 2 possibilities for the sign
of 7, giving us a total of 12 sets of possible population
differences for each site. Changing the sign of 7 is equivalent
to exchanging the X and Y axes of the efg PAS.
rl
+ +
- +
+ -
-
n34
- nl
0.278
-0.278
0.251
-0.251
n34
- n2
0.275
-0.275
0.306
-0.306
n34
- nl
0.027
-0.027
-0.027
0.027
n34
- n2
-0.275
0.275
-0.306
0.306
n34
- nl
-0.031
0.031
0.031
-0.031
n34
- n2
0.256
-0.256
0.325
-0.325
It is commonly assumed that the Si-0 bond is approximately
50% ionic (Le., n34
1.5).33 Therefore, any population
differences in Table 3 that are positive would imply that nl or
n2 (i.e., the “lone pair” populations) would have populations
less than n34 (Le., the “bonding pair” populations). This seems
unreasonable even if x-bonding to the d orbitals of silicon exists.
Therefore, we eliminate those efg orientations and signs with
positive population differences. For case I this leaves only a
negative efg; the magnitude of both n34 - nl and n34 - n2 would
imply a weak x-bonding to the silicon d orbitals that becomes
weaker at smaller Si-0-Si angles. For case I1 only a positive
efg and negative 7 remain, while in case I11 only a negative
efg and negative 7 remain. For both cases I1 and I11 n34 - n1
is near zero for all angles, implying strong x-bonding of the
oxygen p orbital to the silicon d orbitals at all angles, and n34
- 122 varies from -0.290 at 180” to -0.359 at 137.22”,implying
a weaker n-bonding of the oxygen hybrid orbital to the silicon
d orbitals that becomes weaker at smaller Si-0-Si angles.
From eqs 12-17 is it clear that both C,/C,z,
and 7CqlCqz1
will vary linearly as a function offs(@, with slopes and intercepts
that are proportional to the population differences n34 - nl and
n34 - n2. Ignoring for now the slight dependence of the
population differences on the Si-0-Si angle, we can use the
average population differences (see Table 4) in eqs 12-17 to
determine which of the three cases for the efg PAS orientation
best matches the measured quadrupolar parameters of coesite.
12346 J. Phys. Chem., Vol. 99, No. 32, 1995
1
Grandinetti et al.
0.357
0.40 0.42
0.44
COS
0.46
0.48
0.40 0.42
0.50
e m s e -1)
0.44 0.46 0.48
e/(cos e - 1)
0.50
COS
Figure 5. Plots of (a) C&,ZI and (b) ~ C & I vs fractional s character of the hybrid sp" orbitals. Experimental data are represented by the symbol
0. Solid and dashed lines represent the variations of C&ZI and ~ C & Z Iexpected for the three possible orientations of the efg PAS when using
the average orbital population differences in Table 4.
TABLE 5: Orbital Populations Obtained from a Tomes-Dailey Analysis of the 1 7 0 Quadrupolar Coupling Parameters for
the Five Oxygen Sites in Coesite, Assuming the x and z Axes of the Oxygen efg PAS Lie in the Plane of the Si-0-Si Bond with
the x Axis Bisecting the Si-0-Si Bond Angld
01, esl-o-sl= 1800, 04, es,-o-s, = 149.530, 03, esl-o-sl= 14.4.460, 02, esl-o-sl= 142.560,
05, esl-o-s,= 137.220,
C, = -6.05 MHz,
C, = -5.52 MHz,
C, = -5.45 MHz,
C, = -5.43 MHz,
C, = -5.16 MHz,
7 = 0.Ooo
7 = 0.169
v = 0.168
7 = 0.166
7 = 0.292
Q
-0.50
-0.75
-1.00
a
nl
n2
n34
1.770 1.770 1.480
1.832 1.832 1.543
1.895 1.895 1.605
nl
n2
n34
nl
n2
n34
nl
nz
n34
nl
n2
n34
1.767
1.830
1.892
1.757
1.820
1.882
1.488
1.550
1.613
1.763
1.826
1.888
1.762
1.825
1.890
1.487
1.550
1.612
1.762
1.824
1.887
1.765
1.827
1.890
1.487
1.549
1.612
1.763
1.825
1.888
1.755
1.817
1.880
1.491
1.554
1.616
Populations are calculated for three different charges,
Q,on oxygen.
In Figure 5a is a plot of C, vsfs(6) for the five oxygen sites in
coesite. From this plot is clear that case 111, where the z axis
of the efg PAS coincides with the MO x axis, can be eliminated.
In Figure 5b is a plot of qCqvsfs(6). From this plot it is clear
that in addition to case 111, case 11can also be eliminated along
with case I where 7 is negative. This leaves only case I where
7 is positive for the orientation of the I7O efg in the Si-0-Si
linkage. Thus, we conclude that the I7O efg in the Si-0-Si
linkage is negative and has a PAS that coincides with the MO
axis system described in eq 1. This is in agreement with that
predicted by Janes and Oldfield.17
By defining the charge on the oxygen atom, Q, according to
Q = 6 - (n,
+ n2 + 2nw)
(24)
we can solve for all three populations:
orbital population analysis of the I7O quadrupolar coupling
parameters for the five oxygen sites in coesite presented in Table
5.
That both nl and n2 are less than 2 suggests that d-p
n-bonding exists between the silicon d orbitals and the lone
pair electrons on oxygen. In order to increase both nl and n2
to a value of 2 in the Townes-Dailey analysis, it would be
necessary to increase the charge Q. As can be seen in Table 5,
increasing the charge leads to unrealistic values for n34 (Le.,
making the Si-0 bond > 50% ionic) before nl and n2 reach 2.
Therefore, our analysis supports a model where d-p bonding
exists; however, since nl and n2 do not appear to vary
significantly as a function of angle, the d-p n-bonding is not
structurally ~ignificant~~
and is more consistent with the constant
overlap model as described by Janes and Oldfield," as predicted
by the ab initio calculations of Lindsay and Tossell.Io
5. Discussion
[
n2 = iCJCq21 -
1'"
-
2 m
- Q/4 4- 3/2 (25)
Stewart and Spackman reported pseudoatom oxygen charges
of -0.5 14 f 0.048 obtained from the X-ray charge density map
of low quartz.34 Newton and Gibbs* calculated a charge of
-0.65 esu for oxygen in a Si02 moiety of the low quartz
structure in an STO-3G* ab initio MO calculation that included
the 3d AO's of Si. We will assume charges of -0.5, -0.75,
and - 1 esu for oxygen to obtain the complete Townes-Dailey
Given the sign and orientation of the efg obtained from the
above analysis of the coesite data, it appears that nl and n2 are
approximately equal and a simpler form can be obtained for
the correlation between C, and the Si-0-Si angle
and between 7 and the Si-0-Si
where
n12 = n1
= n2.
angle
I7O NMR of Si02 Polymorph Coesite
0.8
J. Phys. Chem., Vol. 99,No. 32, 1995 12347
1
5.2
5.0
130
140
I50
160
Si-@Si Angle (dcgnn)
170
I80
Figure 6. Plot of q vs Si-0-Si angle. Experimental I7O data for
coesite and cristobalite are represented by the symbols B and 4,
respectively, and the ab initio I7O data for cluster H3Si-O-SiH3” are
represented by the symbol 0. The solid line represents eq 27 and dotdashed line represents eq 28.
The expression for 17, which is independent of orbital
populations, was derived earlier by Stemberg36assuming only
u-bonding in the Si-0-Si linkage. This expression remains
valid even if d-p n-bonding exists as long as nl = n2 and 123
= n4 (Le., eq 27 may not apply for I7O in an asymmetric linkage,
e.g., A1-0-Si, where n3 f n4 or n1 f na). A plot of I7O efg
asymmetry parameters vs Si-0-Si angle for the coesite data
as well as other data is presented in Figure 6. Included on the
plot is the curve of eq 27 as well as the curve of the ab initio
based empirical correlation,”
1
I
/*
,,”
I
/
I30
140
150
160
Si-0-Si Angle (degrees)
170
180
Figure 7. Plot of C, vs Si-0-Si angle. Experimental I7O data for
coesite and cristobalite are represented by the symbols and 4,
respectively, and the ab inirio I7O data for cluster H3Si-O-SiH3’o are
represented by the symbol 0. The dashed line represents eq 26 with
n34 - n12 held at a constant value of 0.29 and Cq21 = 20.88 MHz. The
solid line represents eq 31 with a An0 = 0.29 and C,zl = 20.88 MHz.
The dot-dashed line represents eq 32 with C,(180°) = 6.06 MHz.
other possibilities. Thus, although analytical expressions describing the MO dependence on Si-0-Si angle exist, analytical
expressions for trends in orbital populations or charge with Si0-Si are not as easily derived. Therefore, additional assumptions are necessary to obtain a more quantitative fit of the
Townes-Dailey model to the experimental data. To this end,
we simply introduce the empirical correlation
A n = A nO2
(If coso-1
which we had used previously7 in an I7O DAS study of K2s i 4 0 9 glass. Although both curves are in reasonable agreement
with the experimental data, significant deviations between eqs
27 and 28 occur at angles near 120”, where no experimental
data have yet been obtained.
Although the expression for 9 (eq 27) is independent of orbital
populations, the expression for C, depends linearly on n34 nu. From the coesite data it is apparent that n34 - n12 is slightly
dependent on the Si-0-Si angle. This behavior is also found
in our Townes-Dailey analysis of the quadrupolar parameters
obtained in the ab initio calculations of Tossell and coworkers.”.’0 This angle dependence is not accounted for in
the Townes-Dailey molecular orbital analysis and can arise
from a number of different possibilities. One possibility, that
as the Si-0-Si angle widens to 180” there is an increase in
the n overlap between the silicon d orbitals and the oxygen
“lone pair” sp hybrid orbital (Le. IZy2)) while the n overlap
between the silicon d orbitals and the oxygen “lone pair” p
orbital (Le. 1q1))remains constant, can be ruled out since both
orbital differences n34 - nl and 1134 - n2 vary to the same degree
with angle. One explanation that is consistent with the observed
increase of orbital population differences with Si-0-Si angle
could be that as the Si-0-Si angle widens, the Si-0 u bonds
become more ionic (Le., the charge on oxygen increases), while
the n overlap between the silicon d orbitals and both oxygen
“lone pair” orbitals remains constant. However, another
explanation could be that the orbital population differences are
constant while Cq21 varies with angle. It has been suggested
that Cq21 is slightly charge d e ~ e n d e n t ? ~
c$, = Cq2,(1.2)Q
and therefore, c”,;, would also increase with Si-0-Si angle.
There certainly could be a combination of effects, along with
where An = n34 - n12and A ~ =
Q 0.29 for the Si-0-Si
With this expression we obtain
(!+
Cq= Cq2,An
O2
linkage.
coso-1
Previously,’ we had assumed a simple dependence of C, on
the variation of the oxygen fractional s character with Si-0Si angle given by
C, = C,(18Oo) 2 cos 0
cos 0 - 1
where C,(180°) is equivalent to C,nlAno. A plot of I7O
quadrupolar coupling constants vs Si-0-Si
angle for the
coesite data as well as other data is presented in Figure 7.
Included on the plot are the curves of eq 26 with n34 - n12 held
constant and eqs 31 and 32. Although the curve of eq 26 has
the correct trend of C, with Si-0-Si angle, a more quantitative
agreement is obtained with the curves of eqs 31 and 32. In
general, the Townes-Dailey derived expressions for q (eq 27)
and C, (eq 31) have the advantage of being more directly
connected to the MO picture of the Si-0-Si linkage.
Finally, it is interesting to note that on the basis of the ab
initio calculations of Tossell and co-workers’O.” for the cluster
HsSi-O-SiH3, one might predict for coesite a monotonic
variation of the I7O isotropic chemical shift with Si-0-Si angle
over a range of e 1 0 ppm. The observed variation in coesite
(see Table l), however, is not monotonic with Si-0-Si angle
and varies over a much wider range of 29 ppm. In fact, this
variation constitutes a significant fraction of the total range of
shifts measured to date for 170in crystalline silicates.27 Thus,
although the efg for the five inequivalent oxygens in coesite
can be described, to a good approximation, solely in terms of
their Si-0-Si angle, this doesn’t appear to be the case for the
12348 J. Phys. Chem., Vol. 99, No. 32, 1995
chemical shift tensor. Obviously, other factors are involved.
One possible clue seen in the detailed crystal structure drawings
of refs 38 and 20 may be that the sites which have chemical
shifts of 57, 53, and 58 ppm, Le., sites 0 3 , 04, and 05,
respectively, are part of four rings which are linked together to
form a double crankshaft chain along the (101) axis. In contrast
the sites which have the lower chemical shifts of 29 and 41
ppm, i.e., sites 0 1 and 0 2 , respectively, cross-link these double
crankshaft chains and are part of 6- and 8-ring structures.
Although it has been observed that 29Si chemical shifts in
siloxane ring oligomers are strongly correlated to ring
little is known concerning ring size effects on I7Ochemical shifts
in similar compounds. Clearly, more I7O NMR investigations
of crystalline silicates will be needed before these issues are
fully resolved.
6. Conclusions
Using I7Odynamic-angle spinning and magic-angle spinning,
we have resolved and assigned all five oxygen sites in coesite,
a silica polymorph. We have obtained the quadrupolar coupling
parameters for all sites from anisotropic line shape analysis and
have found that a correlation between Si-0-Si angle and I7O
quadrupolar parameters supports previous theoretical as well
as experimental correlations.
A Townes-Dailey analysis of the data indicates that the sign
of the oxygen efg is negative and that the x and z axes of the
oxygen efg PAS lie in the plane of the Si-0-Si bond with the
x axis bisecting the Si-0-Si bond angle. This is in agreement
with the orientation predicted by Janes and Oldfield.I7 A
Townes-Dailey orbital population analysis suggests that d-p
n-bonding exists between the lone pair valence electrons of
oxygen and the d orbitals of silicon but is not structurally
significant.
These data and their analysis should prove helpful in making
the correlation between the isotropic I7O NMR line shapes and
quadrupolar coupling data obtained from 2D DAS spectra of
silicate glasses and their medium-range structural ~ r d e r . ~ . ~ '
Acknowledgment. The high-pressure synthesis was performed by Steve R. Bohlen at the USGS facility at Menlo Park,
CA. P.J.G. acknowledges helpful discussions with Pierre
Florian and Jim Downs. This work was supported by the
Director of the Office of Energy Research, Office of Basic
Energy Sciences, Materials Sciences Division of the US.
Department of Energy under Contract No. DE-AC03-76SF00098
and by the National Science Foundation, through Grant No.
EAR-9204458 to J.F.S. J.H.B. was supported by a NSF
graduate fellowship and a Camille and Henry Dreyfus start-up
grant. U.W. thanks the Alexander von Humboldt Foundation
for a Feodor Lynen Fellowship.
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